Deleting Particle Settings Data Blocks
I was just searching for an answer to the same question. If the particle system is unused by any object Blender will delete it on quit. However sometimes in complex scenes it can be hard to find the object that has the particle system.
You can remove it in the Outliner workspace by selecting Blender File  to display file data and linked libraries, under Particles you will see all your Particle systems and you can Right click and delete them.